Paper Info
Title
The recognizability of sets of graphs is a robust property
Abstract
Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite congruences. Applications to the construction of efficient algorithms and to the theory of context-free sets of graphs follow naturally. The class of recognizable sets depends on the signature of graph operations. We consider three signatures related respectively to Hyperedge Replacement (HR) context-free graph grammars, to Vertex Replacement (VR) context-free graph grammars, and to modular decompositions of graphs. We compare the corresponding classes of recognizable sets. We show that they are robust in the sense that many variants of each signature (where in particular operations are defined by quantifier-free formulas, a quite flexible framework) yield the same notions of recognizability. We prove that for graphs without large complete bipartite subgraphs, HR-recognizability and VR-recognizability coincide. The same combinatorial condition equates HR-context-free and VR-context-free sets of graphs. Inasmuch as possible, results are formulated in the more general framework of relational structures.
Year
DOI
Venue
2005
10.1016/j.tcs.2005.03.018
Computing Research Repository
Keywords
DocType
Volume
hyperedge replacement,quantifier-free definable operation,context-free set,general framework,vertex replacement,finite graph,recognizable set,robust property,graph operation,finite congruence,modular decomposition,flexible framework,locally finite congruence,graph algebra,recognizable set of graphs,context-free graph grammar
Journal
abs/cs/060
Issue
ISSN
Citations 
2-3
Theoretical Computer Science
18
PageRank 
References 
Authors
0.84
35
2
Name
Order
Citations
PageRank
Bruno Courcelle13418388.00
Pascal Weil2717.01